对非线性热传导方程行波解的推广

The extension of travelling wave solutions for the nonlinear heat conduction equation

将非线性热传导方程的行波解推广到了耦合的热传导方程组和广义热传导方程的行波解,其方法主要是利用Riccati方程和Mathematica工具.从而将非线性热传导方程的行波解大大推进了一步.广义热传导方程中的r只要是不等于零就行,同时也推广了行波解的种类,即α≠0时的情形.因此这个结果更具有一般性.

In this paper, we extend the nonlinear heat conduction equation into a coupled heat conduction equation system and generalized heat conduction equation, and its traveling wave solutions are found. We take advantage of Riccati equation and Mathematica software so that the travelling wave solutions of the nonlinear heat conduction equation are greatly improved, only if the r in (1.4) isn't zero. At the same time, we extend the kinds of travelling wave solutions as a≠0. Therefore, our results are more universal.